Math Answers

Six years ago Olwethu lent Happy R150 000 on condition that he would pay her back in nine years time. The applicable interest rate is 15,5% per year, compounded monthly. Happy also owes Olwethu another amount of R250 000 that he has to pay back six years from now for a loan that earned interest at 16,4% per year, compounded semi-annually. Happy asks Olwethu if he an settle both his debts three years from now. The total amount that Happy will have to pay Olwethu three years from now is

A sample of 40 children from Kafue state showed that the mean time they spend watching television is 28.50 hours per week with a standard deviation of 4 hours. Another sample of 35 children from Chilanga showed that the mean time spent by them watching television is 23.5 hours per week with a standard deviation of 5 hours. Using a 2.5% significance level, can you conclude that the mean time spent watching television by children in Kafue state is greater than that for children in Chilanga? Assume that the standard deviations for the two populations are equal [10 marks] Question 

Question 1

The lifetimes of light bulbs produced by a particular manufacturer have a mean of 1,200 hours and a standard deviation of 400 hours. The population distribution is normal. Suppose that you purchase nine bulbs, which can be regarded as a random sample from the manufacturer’s output

a. What is the mean of the sample mean life?

b. What is the variance of the sample mean?

c. What is the standard error of the sample mean?

d. What is the probability that, on average, those nine light bulbs have lives of fewer

than 1,050 hours?

An interest rate of 14,90% per year,

compounded every 3 months. What is equivalent interest rate compounded weekly?

2x+y-z=8

-3x-y+2z=-11

-2x+y+2z=-3

Let R1 and R2 be two relation on real number such that R1 = {(x, y)|x < y} and R2 =

{(x, y)|x > y}, then find R1 ∪ R2,R1 ∩ R2,R1 − R2, R2 − R1, and R1

LR2.

There are 7 defective light bulbs in a bin containing 80 light bulbs. In how many ways can you select at least 6 defective light bulbs when you choose 8 light bulbs at random?

Find the 𝑛th order differential coefficient of 𝑦 = sin 𝑥 log(𝑎𝑥 + 𝑏).

Pamela borrows an amount of money for emergency house repairs. The interest on the loan is compounded quarterly. After four years the debt accumulated by R7980,00 to the amount of R32923,00. The yearly interest rate, expressed as a percentage and rounded to two decimal places, at which the money was borrowed, is

Pamela borrows an amount of money for emergency house repairs. The interest on the loan is compounded quarterly. After four years the debt accumulated by R7980,00 to the amount of R32923,00. The yearly interest rate, expressed as a percentage and rounded to two decimal places, at which the money was borrowed, is